%5E2%2F3%5E-2-simplified.jpeg "(3^5)^2/3^-2 Simplified")
Simplified Form of (3^5)^2/3^-2
In this article, we will simplify the expression (3^5)^2/3^-2 using the rules of exponents.
Rule of Exponents
Before we dive into the simplification process, let's recall the rules of exponents:
- Product of Powers:
a^m * a^n = a^(m+n) - Power of a Power:
(a^m)^n = a^(mn) - Quotient of Powers:
a^m / a^n = a^(m-n) - Zero Exponent:
a^0 = 1 - Negative Exponent:
a^-n = 1/a^n
Simplifying the Expression
Now, let's simplify the expression (3^5)^2/3^-2:
(3^5)^2/3^-2
Using the Power of a Power rule, we can rewrite the expression as:
3^(5*2)/3^-2
3^10/3^-2
Next, we can use the Quotient of Powers rule to simplify the expression further:
3^(10-(-2))
3^12
Therefore, the simplified form of (3^5)^2/3^-2 is:
3^12
Conclusion
In this article, we have successfully simplified the expression (3^5)^2/3^-2 using the rules of exponents. The final answer is 3^12.
